The present invention relates to the predistortion of a modulated signal from one or more sources (also denoted single-carrier and multicarrier transmission, respectively) prior to its transmission over a wired or wireless channel, with the purpose of reducing the distortion incurred by the signal from the transmission over the channel. An example of such a channel is a relayed communication channel (such as a satellite communication channel), whereby optimal relay resources usage requires using the amplifier at the relay (e.g., the satellite amplifier) at or close to its saturation point. Under these circumstances, the transmitted signal typically incurs distortion, reducing the communication reliability. Another example is relayed or non-relayed transmission (wired or wireless) where the high power amplifier (HPA) in the transmitter is used close to its saturation point in order to save costs on this power amplifier.
The transmitter output in a digital communication system can be seen as a baseband waveform. In the case of one source, the waveform is a pulse train modulated by a sequence of complex symbols. This modulation is typically performed by applying the symbols to a pulse shaping filter (PSF). In an operation referred to as mapping each symbol is selected from an allowed set of complex values, represented by an in-phase and quadrature component (I and Q, respectively). The selected symbol depends on the bits corresponding to the source. The set of possible symbols is called a constellation, further referred to as “system constellation”, as it is the constellation used for mapping in the transmitter and demapping in the receiver. Several mapping strategies can be envisaged, including quadrature amplitude modulation (QAM), phase shift keying (PSK) and amplitude and phase shift keying (APSK). These mapping strategies employ different types of system constellations. For example, in the APSK mapping scheme the constellation points are located on two or more concentric rings. Mapping schemes are generally disclosed in a transmission standard, such as ETSI EN 302 307 v1.2.1: Second generation framing structure, channel coding and modulation systems for Broadcasting, Interactive Services, News Gathering and other broadband satellite applications. In the remainder of this text this reference is referred to as the DVB-S2 standard. The combination of a system constellation and a forward error correcting code (FEC) is referred to as a modulation and coding or a modcod. As different prior art documents often use other notations to denote the same physical entity, the notation is explicitly recalled in this document. The complex (I,Q) values provided to the PSF are referred to as transmit symbols. These symbols may or may not be predistorted by a symbol predistorter. The PSF output is a complex signal and can be applied to a signal predistorter or not. The output of the PSF (and possibly the signal predistorter) is denoted as the pulse-shaped signal. In the case of one source, this pulse-shaped signal equals the transmit signal. In the case of more than one source, a pulse-shaped signal is created for each source. The transmit signal then is a non-linear combination of all pulse-shaped signals. The non-linear combination is often referred to as mixing. The non-linear combination corresponds to translating each pulse-shaped signal to its corresponding carrier frequency after which all translated signals are added.
In FIG. 1 an example of a sample-level transmission link, more specifically a satellite communication link, with its main components is shown. The sample-level transmission link includes the satellite transponder, but also the front-end in the modulator and demodulator (e.g., digital-to-analog converter (DAC) in the modulator, analog-to-digital converter (ADC) in demodulator, I/Q (de-)modulation and amplification). In FIG. 1, the DAC and ADC are included in the I/Q modulator and demodulator, respectively. The transmit signal can be formed by one or more sources. This illustration can be generalized to any relayed communication system by generalizing the satellite to a relay. FIG. 2 illustrates a sample-level transmission link for a non-relayed communication system. The connection between the HPA and low-noise amplifier (LNA) can contain channel impairments such as fading, but it does not have a power amplifier in between. The digital transmitter output in a digital communication system is the transmit signal. In the example structure of FIG. 1 or FIG. 2 the transmit signal is I/Q modulated onto a carrier waveform. Before transmission over the air, the carrier waveform is amplified by the transmitter high power amplifier (HPA), e.g. a ground station HPA for satellite communications. In a relayed communication system, for example satellite communications, the signal is received by the relay. In general, this relay filters and amplifies the signal it receives. In the case of satellite communications, the relay is denoted the satellite's transponder, which operation is illustrated in the simplified schematic drawing of FIG. 3. The transponder's incoming signal is passed to a bandpass input multiplexer filter (IMUX), amplified by a travelling wave tube amplifier (TWTA) and filtered again by a bandpass output multiplexer filter (OMUX). A transponder or a relay may contain other components as well, such as up- and down-converters. The amplifier may be of another type than a TWTA. The relay's output signal travels to a plurality of receivers. One such receiver amplifies the signal through a low-noise amplifier (LNA), I/Q demodulates the amplified signal to yield the complex receive signal. For decoding one of the sources, the receive signal is typically provided to a receive filter (typically a PSF) that, after decimation, outputs the received symbols corresponding to that source. When referring to a sample-level transmission link in the following, the structures shown in FIG. 1 and FIG. 2 are referred to. Both structures have one element in common, i.e., at least one high power amplifier (an HPA and/or a TWTA) is present in the transmission link, which can deform the transmit signal in a non-linear way.
In the absence of channel distortion and noise, the receive signal is equal to the transmit signal. On a sample-level transmission link of practical use, however, the non-linear channel changes the phase and amplitude of the transmit signal as it passes through the sample-level transmission link, and thus generate distortion.
The non-linearities of the sample-level transmission link can be modelled by an AM/AM and AM/PM curve, where AM and PM refer to the magnitude and phase of a complex signal, respectively. The AM/AM curve reflects the magnitude of the receive signal versus the magnitude of the transmit signal and the AM/PM curve returns the phase rotation of the transmit signal incurred during amplification in the sample-level transmission link versus the magnitude of the transmit signal. The absolute phase of the receive signal at a particular time instance thus equals the phase of the transmit signal at the corresponding time instance plus the phase rotation applied by the channel. These AM/AM and AM/PM curves are often normalized, such that the saturation point (i.e. the maximum) of the AM/AM curve is (1,1). The ordinate and abscissa of such normalized curves are then the inverses of the output backoff (OBOlin) and input backoff (IBOlin) of the amplifier (e.g. the on-board TWTA for satellite communications or the transmit HPA for non-relayed communications), respectively. Note that in the case of multiple sources, IBO and OBO refer to the global input backoff and global output backoff, respectively. The subscript lin refers to the fact that here these values are shown in linear scale. An example of AM/AM and AM/PM curves is given in FIG. 4. The normalized input amplitudes smaller than 1 are referred to be “before saturation”, while the input amplitudes greater than 1 are referred to be beyond or after saturation.
As will be shown, the behaviour of the AM/AM curve after having reached the saturation point (i.e., the (1,1) point) can be very important in the application of certain predistortion techniques. Especially the extent of the drop (also called fall-back) of the AM/AM curve after saturation has a large impact on the performance. When the drop is large, i.e., when the AM output decreases a lot for increasing AM input, the AM/AM curve is said to have a significant “fall-back” after saturation.
The distortion caused by the non-linear part of the channel is best illustrated by considering the symbol-level transmission link. The symbol-level transmission link includes the transmit and receive PSFs and is thus the channel seen between the transmit and receive symbols. The distortion caused by the symbol-level transmission link is illustrated by plotting the location of the received symbols of one source in the absence of channel noise, which is referred to as a scatter plot at the receiver side (in the following, simply called a “scatter plot”). The distortion mainly has two consequences:
(1) in a scatter plot each constellation point becomes a cluster, caused by inter-symbol interference (ISI) due to the memory (caused by the filters, such as IMUX, OMUX, and PSFs) in the channel, and
(2) constellation warping occurs, which causes the mass points of the clusters to be no longer on the original system constellation grid.
Such a scatter plot for the third source, for the channel given in FIG. 4, and for four sources of 7.5 Mbaud, 20% roll-off and 32-APSK rate 5/6 from the DVB-S2 standard, is illustrated in FIG. 5.
Techniques to mitigate the distortion effects, caused by the saturated amplifier (e.g. the transmitter HPA or the TWTA in the satellite transponder), by manipulating the transmit symbols or the transmit signal in the transmitter are generally referred to as pre-distortion. Note that an important difference between satellite TWTA predistortion and transmitter HPA predistortion is that the wireless link towards the TWTA should comply with a spectral mask which limits the occupied bandwidth of the predistorted signal. Almost all predistortion techniques in this document apply both for transmitter HPA and satellite TWTA predistortion. It will clearly be indicated below when a certain technique is only applicable to one of both. Especially in a broadcasting context, predistortion can yield significant gains because one predistorter in the transmitter can improve the performance of millions of terminals receiving the signal from the transmitter. The first publications on predistortion date from the 1970s (see amongst others “Modeling and Performance Evaluation of Nonlinear Satellite Links—A Volterra Series Approach”, Benedetto at al., IEEE Tr. on Aerospace and Electronic Systems, Vol. AES-15, No. 4, pp. 494-507, July 1979 and “Adaptive Cancellation of Nonlinear Intersymbol Interference for Voiceband Data Transmission”, Biglieri et al., IEEE J. Sel. Areas In Comm., Vol. SAC-2, No. 5, pp. 765-777, September 1984). Early and recent publications focused especially on a Volterra series representation of the non-linear channel with memory. In general, prior art predistortion techniques introduce a circuit in the transmitter that generates “anti-distortion” for the distortion caused by the channel. The combination of the distortion from the channel and the “anti-distortion” generated at the transmitter ideally should minimize the overall distortion at the receiver. The most relevant techniques can be classified in two categories: signal predistortion (also known as fractional predistortion or sample-level predistortion) and symbol predistortion (also known as data predistortion). Symbol predistortion aims at subtracting from the transmitted symbols the interference expected at the receive side. This can for example be done by (statically or dynamically) computing a new constellation from which the transmitted symbols are selected, while maintaining the original system constellation for demapping at the receiver. The new constellation can for example be a non-linear transformation of the original system constellation (in the case of static symbol predistortion). Signal predistortion aims at performing the inverse operation of the sample-level transmission link on the signal provided by the PSF. Ideally, the inverse operation of the sample-level transmission link and the sample-level transmission link itself are applied consecutively on the transmit signal, as illustrated in FIG. 6. In the ideal case the corresponding overall AM/AM and AM/PM curves of the cascade of the predistortion unit and the sample-level transmission link are those of a hard-limiter channel, as shown in FIG. 7.
However, performing the inverse operation of the channel on the signal provided by the PSF is a non-linear operation and causes spectral regrowth, i.e., the occupied frequency bandwidth of the transmit signal becomes larger. Until very recently, signal predistortion was thought not to be applicable for relayed communication such as satellite communications, because the spectral regrowth does not comply with the spectral mask on the transmit signal. For example, it is explicitly mentioned that fractional predistortion cannot be used in satellite communications in U.S. Pat. No. 6,963,624B1 and in the papers “Constellation Design for Transmission over Nonlinear Satellite Channels” (Montorsi et al., IEEE Global Communications Conference (GLOBECOM), pp. 3401-3406, December 2012) and “Joint precoding and predistortion techniques for satellite telecommunication systems” (M. Álvarez-Diaz et al., Int'l Symp. on Wireless Communication Systems, September 2005, pp. 688-692). In EP2922217 A1 solutions for the spectral regrowth caused by the inverse operation have been proposed. That is, a low-pass filter is used after the “inverse of the sample-level transmission link” block to filter out the spectral regrowth. The low-pass filter can be a second PSF (which essentially is a low-pass filter), but is not limited to this.
A system level block diagram for two sources with signal predistortion is shown in FIG. 8. For each source, incoming digital data, referred to as a sequence of information bits, is encoded with a forward error correcting code encoder. This encoder can be a single encoder, but can also be the concatenation of several encoders. The encoder output is a stream of coded bits which are mapped to symbols belonging to a certain system constellation, such as PSK, APSK or QAM. This system constellation is agreed upon by transmitter and receiver. The sequence of complex transmit symbols is denoted a. In the case of having more than one source, as in FIG. 8, the sequence of complex symbols is denoted ai for source i. The system constellation does not need to be the same for each source (e.g., when each source has different throughput requirements). When applying signal predistortion, the transmit symbols are provided to the PSF, the pulse-shaped signals are combined, followed by a signal predistorter yielding a(t), which is sent over the sample-level transmission link. The demodulator locks on one of the sources. Only one demodulator is shown, but of course, multiple demodulators can be present, at the same location or at another location. At the receiver, corresponding to a particular source, the receive signal r(t) is provided to the receive filter (which is typically a PSF) yielding the sequence of receive symbols r, which is demapped, typically using the corresponding system constellation as a reference. The demapper outputs for example likelihood ratios of the coded bits, which are next fed to the decoder. Like the encoder, the decoder can be composed of one or more concatenated decoders. A person skilled in the art of digital receivers will readily understand that one or more decoders can process the received information in an iterative manner and one or more decoders can also exchange information with the demapper in an iterative fashion.
Below symbol predistortion will be elaborated, because in the prior art the performance of signal predistortion is significantly lower than that of the recent symbol predistortion techniques, especially for linearized channels, which become omnipresent because today most of the amplifiers are linear.
FIG. 9 shows an example communication system using symbol predistortion in the presence of two sources. When applying symbol predistortion, the system constellation symbols a are provided to a symbol predistorter, yielding a′. The symbols at the output of the symbol predistorter see the symbol-level transmission link, which includes the PSFs at the transmit and receive side.
High performance symbol predistortion is complex in logic and/or memory, especially for higher order system constellations. In most of the literature it is argued that system constellations larger than 32-APSK cannot be predistorted using symbol predistortion.
For the above-mentioned reasons predistortion was not much applied in satellite communications, despite it being a relatively long studied problem. Only recently, some prior art techniques, e.g. also disclosed in EP1129556 B1, EP1371202 B1, EP1374517 B1, WO2014/122080 A1, U.S. Pat. No. 8,355,462 B2 and US2015/0311927 and in the paper “Multicarrier Successive Predistortion for Nonlinear Satellite Systems” (Beidas, IEEE Trans. Comm., April 2015, pp. 1373-1382) significantly changed the paradigm of symbol predistortion and have applied symbol predistortion in a memory-efficient way.
The application of symbol predistortion is now discussed more in detail. First a symbol predistorter for one source is elaborated. A prior art predistortion solution as disclosed in WO2014/122080, is shown in FIG. 10. The proposed techniques apply a successive interference cancellation (SIC) technique where multiple SIC stages predict and correct for the distortion. Iteratively, the distortion error is reduced towards zero. The structure contains several quasi-identical stages, whereby each stage applies a correction on the transmitted symbols. Each stage is called a successive interference cancellation (SIC) stage. Each SIC stage comprises a correction path containing a model of the symbol-level transmission link, which mimics the effect of the full symbol-level transmission link on multiple (for multiple sources) sequences of transmitted digital symbols. The correction term applied in a SIC stage is based on some function of the symbol value at the symbol-level transmission link model output and the corresponding symbol of a predefined constellation. As an example, the predefined constellation can be a simple scaling of the system constellation. For this example, and when referring to a “corresponding” symbol of the predefined constellation, this corresponding symbol is then also a simple scaling of the symbol from the system constellation at the symbol predistorter input. Advantageously said function is the difference between the symbol value at the transmission link model output and the corresponding symbol of the predefined constellation. FIG. 11 shows how the correction term is calculated in this prior art solution. The symbol-level transmission link model is also called forward model in the prior art.
The usage of a symbol predistorter is also possible in case of multiple sources, as proposed in U.S. Pat. No. 8,355,462 B2 and US2015/311927. For such a multiple source system, the block diagrams in FIG. 10 and FIG. 11 needs to be adapted, as can be seen in FIG. 12 and FIG. 13.
However, simulations show that these techniques are still very sensitive to the saturation of the amplifier, and even more sensitive to the fall-back of the AM/AM curve after saturation, which still gives room for improvement.
The sensitivity of predistortion techniques to amplifier saturation can be illustrated through scatter plots. In EP1129556 B1 and EP1371202 B1 it is clear that the outer points in a scatter plot exhibit a tail effect. This is explicitly mentioned in EP1129556 B1: “the corner points, which are at TWT saturation, exhibit a corner tail effect. This is due to the fact that, at these points, the gain of the TWT is zero and perfect convergence is not possible.” In EP1374517 B1 it was tried to solve this tail effect, but it is clear from FIG. 10 in that document that the tail effect is still preserved. Note that U.S. Pat. No. 8,355,462 B2 mentions a method denoted “Hard limiter per carrier”, which removes all amplitude information from the waveform after the transmit filter. This of course will not work with amplitude modulation, e.g. multiple ring constellations such as 16-APSK and higher (e.g. 32-APSK, . . . , 256-APSK).
In EP1374517 B1 the forward model was modified with respect to the actual symbol-level transmission link in order to improve the convergence of the distortion error towards zero in the multiple SIC stages. More specifically, the adopted AM/AM curve in the model does not fall back anymore beyond saturation. On the contrary, it increases with the bisector beyond the saturation point. FIG. 14 illustrates that the distortion error within the multiple SIC stages converges towards zero, except for some exceptional points, using this technique for the TWTA with characteristics as in FIG. 3. However, the actual distortion error when transmitting the predistorted symbols over the actual symbol-level transmission link is still significant (see FIG. 15), because the transmitted waveform still goes significantly beyond saturation of the actual sample-level transmission link.
Hence, the performance gains of symbol predistortion with multiple SIC stages is poor for channels with significant fall-back after saturation. Consequently, there is a need for an extension of symbol predistortion with multiple SIC stages on channels with fall-back after saturation.